报告题目：Riordan arrays, the Riordan group, and their extensions and applications

报告人：Tian-Xiao He，Illinois Wesleyan University, USA

报告时间：2026年5月13日（周三）16:00-17:00

报告地点：20-306

报告摘要：In this talk, we introduce Riordan arrays, multiple Riordan arrays, and multiple almost-Riordan arrays using combinatorial object enumeration and lattice paths. All Riordan arrays, all multiple Riordan arrays, and all double approximate Riordan arrays constitute three groups, respectively called the Riordan group, the multiple Riordan group, and the multiple approximate Riordan group. We also present the sequence characteristics of these Riordan arrays and their production matrices. We define the compression of multiple Riordan arrays and multiple almost-Riordan arrays and give their sequence characteristics. We investigate the totla positivity of the compression of multiple Riordan arrays and multiple almost-Riordan arrays. Finally, we discuss the representation of the orthogonal polynomial sequence and its three-dimensional extension using the production matrices of the corresponding Riordan arrays. Time permitting, we will propose the embeddability of Coxeter groups to Riordan groups, as well as a unified combinatorial and algebraic framework connecting wavelet systems and Riordan group operators.

报告人简介：Tian-Xiao He, Professor of Mathematics and the Beling Endowed Professor of Natural Sciences and Mathematics at Illinois Wesleyan University, earned his Doctor of Science degree from Dalian University of Technology in 1987 and his Doctor of Philosophy degree from Texas A&M University in 1991. He has been a faculty member at Illinois Wesleyan University since 1991. His research interests include spline functions, approximation theory, wavelet analysis, numerical analysis, enumerative combinatorics, and some topics in computational mathematics.  Professor He has authored over 150 scholarly articles and six books.

邀请人：调和分析及其应用创新团队